(AP P1) Quiz 4.1

An automobile traveling on a straight, level road has an initial speed  $v$  when the brakes are applied. In coming to rest with a constant acceleration, it travels a distance  $x$  . How far would the automobile travel in coming to rest if it had the same acceleration but an initial speed  $2v$  ?

•  $\frac{1}{2}x$  

•  $x$  

•  $2x$  

•  $4x$  

An object is moving to the right with speed  $v_i$  when a force of magnitude  $F$  is exerted on it. In which of the following situations is the object's direction of motion changing and kinetic energy decreasing a the instant shown?

• 
• 
• 
• 

A crate is on a horizontal frictionless surface. A force of magnitude  $F$  is exerted on the crate at an angle  $\theta$  to the horizontal, as shown in the figure above, causing the crate to slide to the right. The surface exerts a normal force of magnitude  $F_N$  on the crate. As the crate slides a distance  $d$  , it gains an amount of kinetic energy  $\Delta K$  . While  $F$  is kept constant, the angle  $\theta$  is now doubled but is still less than  $90\degree$  . Assume the crate remains in contact with the surface.

As the crate slides a distance  $d$  , how does the new gain in kinetic energy compare to  $\Delta K$  ?

• The new gain is greater than  $\Delta K$  

• The new gain is less than  $\Delta K$  

• The new gain is equal to  $\Delta K$  

• The new gain is greater or less than  $\Delta K$  depending on the value of  $\theta$  

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity  $v$  as a function of time  $t$  is shown in the graph above. The five labeled points divide the graph into four sections.

During some part of the motion, the work done on the cart is negative. What feature of the motion indicates this?

• The speed is increasing

• The speed is decreasing

• The acceleration is positive

• The acceleration is negative

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity  $v$  as a function of time  $t$  is shown in the graph above. The five labeled points divide the graph into four sections.

For which segment does the cart move the greatest distance?

• AB

• BC

• CD

• DE

A block on a horizontal surface is placed in contact with a light spring with spring constant $k$  , as shown in figure 1. When the block is moved to the left so that the spring is compressed a distance  $d$  from its equilibrium length, the potential energy stored in the spring-block system is  $E_m$  . When a second block of mass  $2m$  is placed on the same surface and the spring is compressed a distance  $2d$  , as shown in figure 2, how much potential energy is stored in the spring compared to the original potential energy  $E_m$  ? All frictional forces are considered to be negligible.

•  $\frac{1}{2}E_m$  

•  $E_m$  

•  $2E_m$  

•  $4E_m$  

In which of the following situations is the kinetic energy of the object decreasing?

• A sphere is dropped from a building

• A satellite is moving in a circular orbit around Earth

• A baseball is heading upward after being thrown at an angle

• An elevator is moving upward at a constant velocity

A block of mass  $M$  is sliding with an initial speed  $v_i$  along a horizontal surface with negligible friction. A constant force of magnitude  $F_A$  is exerted on the object at an upward angle of  $60\degree$  from the horizontal, causing the object to speed up. If the block remains in contact with the floor, what is the change in the block's kinetic energy as it moves a horizontal distance  $\Delta x$  ?

•  $\frac{1}{2}F_A\Delta x$  

•  $F_A\Delta x$  

•  $\frac{1}{2}Mv_i^2+\frac{1}{2}F_A\Delta x$  

•  $\frac{1}{2}Mv_i^2+F_A\Delta x$  

Three identical rocks are launched with identical speeds from the top of a platform of height  $h_0$  . The rocks are launched in the directions indicated above.

Rock 1, of mass  $m$  , reaches a maximum height  $h_{\max}$  after being launched. During the time between the instant rock 1 is launched from height  $h_0$  and the instant it returns to height  $h_0$  , the work done on the rock by the gravitational force is

• 0

•  $-mgh_0$  

•  $-mg\left(h_{\max}-h_0\right)$  

•  $2mg\left(h_{\max}-h_0\right)$  

A cart is moving on a level track in the positive  $x$ -direction. A force acting parallel to the  $x$ -axis is exerted on the cart. The graph above shows the net force exerted on the cart as a function of displacement. As the cart travels from  $x=0$  m to  $x=4$  m, what is the net change in the kinetic energy of the cart?

• An increase of 20 J

• An increase of 10 J

• A decrease of 20 J

• A decrease of 10 J