SID: Useful
Physics 7A
Midterm 2, Version C
Useful quantities: sin 30o = 1/2, cos 30o =
√
Name/SID:
3/2 = 0.866, sin 450 = cos 45o = 0.707.
1. (a) (2 points) A dart is loaded into a spring-loaded toy dart gun by pushing the spring in by a distance d. For the next loading, the spring is compressed a distance 2d. How much work is required to load the second dart compared to that required to load the first? A. one-half as much B. one-quarter as much C. the same D. four times as much (a) (b) (2 points) A coin is placed 30 cm from the center of a rotating, horizontal turntable. What force causes the centripetal acceleration when the coin is stationary relative to the turntable? A. gravitational force B. normal force C. static friction D. inertia
(b) (c) (2 points) A unit of work, 1 J is equal to A. 1N · m. B. 1 N · m2 . C. 1 mkg 3 ·s2 . D. 1 kg·m . s2 (d) (2 points) A force F = 60 N applied to a spring stretches it by ∆x = 15 cm. The spring constant is A. 0.25 N/m. B. 40 N · m. C. 4N/m. D. 400 N/m.
(d)
Physics 7A
Midterm 2, Version C
Name/SID:
(e) (2 points) A ball of mass m is suspended on a string of length R from the ceiling of a train car. At time t = 0 the car has speed v and acceleration a. To decscribe the forces acting on the ball, a non-inertial observer riding in the car needs to introduce a fictitious force of magnitude A. F = mg. B. F = 0. 2 C. F = m vR . D. F = ma. (e) 2. (5 points) Three blocks are in contact on a frictionless horizontal surface. The blocks are accelerated by a single horizontal force F = 30 N . Find the acceleration of each block and the contact force of block 2 on block 3 if masses of the blocks are m1 = 3 kg m2 = 2 kg, and m3 = 1 kg.
~ = −2ˆi − 3ˆj and B ~ = 3ˆi − 5ˆj find 3. (5 points) For two vectors, A ~ ·B ~ (a) the scalar product, A
(b) the angle between the vectors.
Physics 7A
Midterm 2, Version C
Name/SID:
4. (10 points) A block (mass m = 6 kg) is placed on a rough rotating platform at a distance R = 0.5m from the rotation axis as shown in the figure below. The block is held stationary relative to the platform by the force of friction. The coefficient of the static friction between surfaces of the platform and the block is µs = 0.25 and the coefficient of the kinetic friction is µk = 0.20.
(a) Draw a free body diagram and label all the forces.
(b) Find the friction force if the platform makes 10 revolutions per minute.
Physics 7A
Midterm 2, Version C
Name/SID:
(c) What is the maximal speed and rotation rate before the block begins to slide?
5. (15 points) A wooden block of mass m = 6kg is placed at the bottom of a frictionless incline (angle θ = 45.0o with the horizontal) and is given initial velocity v = 2.5 m/s up the incline. (a) Draw a free body diagram.
(b) Find all the forces acting on the block and its acceleration
Physics 7A
Midterm 2, Version C
Name/SID:
(c) Find the distance the block will move along the inclined surface before it stops momentarily.
6. (15 points) In the figure below, m2 = 10 kg, θ = 30.0o , the coefficient of static friction between the block and the incline is µs = 0.25 and the coefficient of kinetic friction is µk = 0.20.
(a) Draw free body diagrams for both blocks. Explain how does the direction of the friction force acting on block 2 depends on value of m1 .
Physics 7A
Midterm 2, Version C
Name/SID:
(b) Find the range of possible values of m1 for which the system will be in static equilibrium.
(c) If m1 is equal to the minimum value found in part (b) and you nudge block 2 slightly downward, will it continue to slide? If so, what will be its acceleration? (HINT: the coefficient of kinetic friction is smaller than the coefficient of static friction.)
Physics 7A
Midterm 2, Version C
Name/SID:
Midterm 2, Version C
Useful quantities: sin 30o = 1/2, cos 30o =
√
Name/SID:
3/2 = 0.866, sin 450 = cos 45o = 0.707.
1. (a) (2 points) A dart is loaded into a spring-loaded toy dart gun by pushing the spring in by a distance d. For the next loading, the spring is compressed a distance 2d. How much work is required to load the second dart compared to that required to load the first? A. one-half as much B. one-quarter as much C. the same D. four times as much (a) (b) (2 points) A coin is placed 30 cm from the center of a rotating, horizontal turntable. What force causes the centripetal acceleration when the coin is stationary relative to the turntable? A. gravitational force B. normal force C. static friction D. inertia
(b) (c) (2 points) A unit of work, 1 J is equal to A. 1N · m. B. 1 N · m2 . C. 1 mkg 3 ·s2 . D. 1 kg·m . s2 (d) (2 points) A force F = 60 N applied to a spring stretches it by ∆x = 15 cm. The spring constant is A. 0.25 N/m. B. 40 N · m. C. 4N/m. D. 400 N/m.
(d)
Physics 7A
Midterm 2, Version C
Name/SID:
(e) (2 points) A ball of mass m is suspended on a string of length R from the ceiling of a train car. At time t = 0 the car has speed v and acceleration a. To decscribe the forces acting on the ball, a non-inertial observer riding in the car needs to introduce a fictitious force of magnitude A. F = mg. B. F = 0. 2 C. F = m vR . D. F = ma. (e) 2. (5 points) Three blocks are in contact on a frictionless horizontal surface. The blocks are accelerated by a single horizontal force F = 30 N . Find the acceleration of each block and the contact force of block 2 on block 3 if masses of the blocks are m1 = 3 kg m2 = 2 kg, and m3 = 1 kg.
~ = −2ˆi − 3ˆj and B ~ = 3ˆi − 5ˆj find 3. (5 points) For two vectors, A ~ ·B ~ (a) the scalar product, A
(b) the angle between the vectors.
Physics 7A
Midterm 2, Version C
Name/SID:
4. (10 points) A block (mass m = 6 kg) is placed on a rough rotating platform at a distance R = 0.5m from the rotation axis as shown in the figure below. The block is held stationary relative to the platform by the force of friction. The coefficient of the static friction between surfaces of the platform and the block is µs = 0.25 and the coefficient of the kinetic friction is µk = 0.20.
(a) Draw a free body diagram and label all the forces.
(b) Find the friction force if the platform makes 10 revolutions per minute.
Physics 7A
Midterm 2, Version C
Name/SID:
(c) What is the maximal speed and rotation rate before the block begins to slide?
5. (15 points) A wooden block of mass m = 6kg is placed at the bottom of a frictionless incline (angle θ = 45.0o with the horizontal) and is given initial velocity v = 2.5 m/s up the incline. (a) Draw a free body diagram.
(b) Find all the forces acting on the block and its acceleration
Physics 7A
Midterm 2, Version C
Name/SID:
(c) Find the distance the block will move along the inclined surface before it stops momentarily.
6. (15 points) In the figure below, m2 = 10 kg, θ = 30.0o , the coefficient of static friction between the block and the incline is µs = 0.25 and the coefficient of kinetic friction is µk = 0.20.
(a) Draw free body diagrams for both blocks. Explain how does the direction of the friction force acting on block 2 depends on value of m1 .
Physics 7A
Midterm 2, Version C
Name/SID:
(b) Find the range of possible values of m1 for which the system will be in static equilibrium.
(c) If m1 is equal to the minimum value found in part (b) and you nudge block 2 slightly downward, will it continue to slide? If so, what will be its acceleration? (HINT: the coefficient of kinetic friction is smaller than the coefficient of static friction.)
Physics 7A
Midterm 2, Version C
Name/SID:
