Question

A 40.0kg wagon is being towed up a hill by an elf inclined at 18.5 degrees with respect to the horizontal. The tow rope is parallel to the incline and exerts a force of 140 N on the wagon. Assume that the wagon starts from rest at the bottom of the hill, and disregard friction. What is the acceleration of the wagon up the hill?

A. 1.8 m/s^2
B. 2.5 m/s^2
C. .58 m/s^2
D. 0.38 m/s^2​

Answer 1

To find the acceleration of the wagon up the hill, resolve the applied force into components. Use Newton's second law to calculate the acceleration. The correct answer is D. 0.38 m/s².

Step-by-step explanation:

To find the acceleration of the wagon up the hill, we need to resolve the force applied by the tow rope into components. The force component along the incline will contribute to the acceleration while the force component perpendicular to the incline will be balanced out by the normal force.

The force component along the incline is given by F_parallel = F * sin(θ), where F is the force applied by the tow rope and θ is the angle of the incline. Plugging in the values, we get F_parallel = 140 N * sin(18.5°).

Next, we can calculate the acceleration using Newton's second law: F_parallel = m * a, where m is the mass of the wagon and a is the acceleration.

Rearranging the equation, we have a = F_parallel / m. Substituting the values, we get a = (140 N * sin(18.5°)) / 40.0 kg.

Using a calculator, the acceleration is approximately 0.38 m/s². Therefore, the correct answer is D. 0.38 m/s².