(i) C (ii) B
Phys 135A Midterm 2 Solutions Be neat and show all work to get full credit
Nov. 13, 2008
1-(i) B
(ii) B
2-) (i) C
(ii) B
1
3- A small box of mass 5 kg is attached to a big box of mass 15 kg with a light glue as shown in the figure below. When an external force of magnitude 200 N is being applied to the small box from the left, the system of boxes begins to move to the right. Given the fact that there is no friction on the surface, calculate (a) the acceleration of the system (b) the force that the big box applies on the small box.
Solution: (b)First, show the all the horizontal forces on the small one, then apply Newton’s 2nd law along the direction of motion!
4- A box of mass 40 kg is exerted a force of 600 N as shown below. The box starts moving on a surface with kinetic friction coefficient of 0.2. What is the acceleration of this box?
Solution: First things first: The free body diagram would be:
Applying the 2nd law to x and y directions: x-direction
y-direction 0
Since
2
5- An 18.0-kg box is released on a 37.0º incline and accelerates down the incline at 0.270 m friction force impeding its motion. How large is the coefficient of kinetic friction?
s2 .
Find the
Solution: The free-body diagram is
Applying the Newton’s 2nd law in y-direction, we have Applying the 2nd law in x-direction, we have
The coefficient of kinetic friction can be found from
6- A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm, as shown. If its speed is 4.00 m
s
and its mass is 0.300 kg, calculate the tension in the string when the ball is
(a) passing by the left side of the circle, exactly halfway vertically (b) at the bottom of its path. Solution: (a)
(b)
(mg does not have any projection along the radial direction at this point!)
7- What is the gravitational force at a point where the distance of that point to the center of the Earth is 10 times the radius of the Earth. Express your answer in terms of the gravitational force at the surface of the Earth. Solution: First let us express the gravitational force at the surface of the Earth symbolically:
Now, since we are trying to find the force when the distance gets 10 times bigger, we say
Our answer is that the gravitational force is 100 times smaller than the gravitational force at theEarth’s surface.
3
8- A 330-kg piano on a 28º incline is released free from the top of the incline. The piano is observed to slide down with an acceleration of 1.5 m/s2 for a distance of 3.6 m. Calculate: (a) the friction force, (b) the work done by the friction force, (c) the work done by the force of gravity, and (d) the net work done on the piano. Solution: The free-body diagram will look like the same as in Problem 5 above.
(a) Applying the 2nd law in x-direction, we have thus
(b) (c) (d) 9- A spring is vertically held and a mass of 0.55 kg is attached from it. The spring is observed to stretch a distance of 2 cm, determine the force constant of the spring. Solution:
Because the mass will stretch until the spring force balances the gravity, we have , which gives
10- A toy car of mass of 4 kg has a speed of 2 m/s at point B in the following figure. What would be its speed when it passes by the point (a) C and (b) D?
Solution:
4
(a) From conservation of energy we have . Choosing the dashed line as our gravitational potential energy reference line, in going from point B to point C,
Dividing both sides by m, and multiplying both sides by 2, we get
(b) Again, from
. In going from point B to point D, we have
To simplify this equation (with our eye fixed at
), let us divide both sides by m, multiply by 2:
5
Nov. 13, 2008
1-(i) B
(ii) B
2-) (i) C
(ii) B
1
3- A small box of mass 5 kg is attached to a big box of mass 15 kg with a light glue as shown in the figure below. When an external force of magnitude 200 N is being applied to the small box from the left, the system of boxes begins to move to the right. Given the fact that there is no friction on the surface, calculate (a) the acceleration of the system (b) the force that the big box applies on the small box.
Solution: (b)First, show the all the horizontal forces on the small one, then apply Newton’s 2nd law along the direction of motion!
4- A box of mass 40 kg is exerted a force of 600 N as shown below. The box starts moving on a surface with kinetic friction coefficient of 0.2. What is the acceleration of this box?
Solution: First things first: The free body diagram would be:
Applying the 2nd law to x and y directions: x-direction
y-direction 0
Since
2
5- An 18.0-kg box is released on a 37.0º incline and accelerates down the incline at 0.270 m friction force impeding its motion. How large is the coefficient of kinetic friction?
s2 .
Find the
Solution: The free-body diagram is
Applying the Newton’s 2nd law in y-direction, we have Applying the 2nd law in x-direction, we have
The coefficient of kinetic friction can be found from
6- A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm, as shown. If its speed is 4.00 m
s
and its mass is 0.300 kg, calculate the tension in the string when the ball is
(a) passing by the left side of the circle, exactly halfway vertically (b) at the bottom of its path. Solution: (a)
(b)
(mg does not have any projection along the radial direction at this point!)
7- What is the gravitational force at a point where the distance of that point to the center of the Earth is 10 times the radius of the Earth. Express your answer in terms of the gravitational force at the surface of the Earth. Solution: First let us express the gravitational force at the surface of the Earth symbolically:
Now, since we are trying to find the force when the distance gets 10 times bigger, we say
Our answer is that the gravitational force is 100 times smaller than the gravitational force at theEarth’s surface.
3
8- A 330-kg piano on a 28º incline is released free from the top of the incline. The piano is observed to slide down with an acceleration of 1.5 m/s2 for a distance of 3.6 m. Calculate: (a) the friction force, (b) the work done by the friction force, (c) the work done by the force of gravity, and (d) the net work done on the piano. Solution: The free-body diagram will look like the same as in Problem 5 above.
(a) Applying the 2nd law in x-direction, we have thus
(b) (c) (d) 9- A spring is vertically held and a mass of 0.55 kg is attached from it. The spring is observed to stretch a distance of 2 cm, determine the force constant of the spring. Solution:
Because the mass will stretch until the spring force balances the gravity, we have , which gives
10- A toy car of mass of 4 kg has a speed of 2 m/s at point B in the following figure. What would be its speed when it passes by the point (a) C and (b) D?
Solution:
4
(a) From conservation of energy we have . Choosing the dashed line as our gravitational potential energy reference line, in going from point B to point C,
Dividing both sides by m, and multiplying both sides by 2, we get
(b) Again, from
. In going from point B to point D, we have
To simplify this equation (with our eye fixed at
), let us divide both sides by m, multiply by 2:
5
