Question

Notice that the final answer for the acceleration depends only on g and the angle θ, not the mass. Equation (2), which gives the normal force, isn't useful here, but is essential when friction plays a role.

QUESTION If the car is parked on a more gentle slope, how will the time required for it to slide to the bottom of the hill be affected?

The time would be longer.The time would be shorter.    The time would be the same.

PRACTICE IT

Use the worked example above to help you solve this problem. A car of mass m is on an icy driveway inclined at an angle θ = 23.0°, as shown in the figure.

(a) Determine the acceleration of the car, assuming the incline is frictionless.
m/s²

(b) If the length of the driveway is 23.5 m and the car starts from rest at the top, how long does it take to travel to the bottom?
s

(c) What is the car's speed at the bottom?
m/s

EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK!

(a) Suppose a hockey puck slides down a frictionless ramp with an acceleration of 5.30 m/s². What angle does the ramp make with respect to the horizontal?
°

(b) If the ramp has a length of 5.80 m, how long does it take the puck to reach the bottom?
s

(c) Now suppose the mass of the puck is doubled. What's the puck's new acceleration down the ramp?
m/s²

Answer 1

1]

a] Acceleration of the car assuming no friction will be:

a = gsin23 = 9.8sin23 = 3.8291 m/s²

b] L = 23.5 m

Initial velocity = 0 m/s

use, L = ut + (1/2)at²

=> 23.5 = 0 + (1/2)(3.8291)t²

=> t = 3.503s

c] Car's speed at the bottom will be:

v = u + at

=> v = 0 + 3.8291(3.503) = 13.415 m/s.

2] a]

a = gsin

5.3 = 9.8sin

b] S = ut + (1/2)at²

5.8 = 0 + (1/2)(5.3)t²

=> t = 1.48s.

c] Since the acceleration is independent of the mass of the object, doubling it will not change its acceleration.