Question54. (II) A child on a sled reaches the bottom of a hill with a velocity of $10.0 \mathrm{~m} / \mathrm{s}$ and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg , what is the average retarding force on the sled on the horizontal straightaway?

Studdy Solution

STEP 1

1. The child and sled have an initial velocity of $10.0 \, \text{m/s}$ at the bottom of the hill.
2. The child and sled come to a stop after traveling $25.0 \, \text{m}$ on a horizontal straightaway.
3. The mass of the child and sled together is $60.0 \, \text{kg}$ .
4. We are asked to find the average retarding force on the sled.

STEP 2

1. Identify the known values and the unknown.
2. Use the kinematic equation to find acceleration.
3. Use Newton's second law to find the retarding force.

STEP 3

Identify the known values and the unknown.
- Initial velocity, $v_i = 10.0 \, \text{m/s}$ - Final velocity, $v_f = 0 \, \text{m/s}$ - Distance traveled, $d = 25.0 \, \text{m}$ - Mass, $m = 60.0 \, \text{kg}$ - Unknown: Average retarding force, $F$

STEP 4

Use the kinematic equation to find acceleration.
The kinematic equation that relates initial velocity, final velocity, acceleration, and distance is:
$v_f^2 = v_i^2 + 2a d$
Substitute the known values:
$0 = (10.0)^2 + 2a(25.0)$
Solve for $a$ :
$0 = 100 + 50a$ $50a = -100$ $a = -\frac{100}{50}$ $a = -2.0 \, \text{m/s}^2$

STEP 5

Use Newton's second law to find the retarding force.
Newton's second law states:
$F = ma$
Substitute the known values:
$F = 60.0 \times (-2.0)$ $F = -120.0 \, \text{N}$
The negative sign indicates that the force is acting in the opposite direction of motion, which is expected for a retarding force.
The average retarding force on the sled is:
$\boxed{-120.0 \, \text{N}}$

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