Question

a child in a go - cart with a gross weight of 155 pounds is parked on a 14 slope. what force is required to prevent the child in a go - cart from rolling down the hill? (rounded to four decimals)

Explanation:

Step1: Decompose the weight force

The weight of the child and go - cart is \(W = 155\) pounds. The force that causes the cart to roll down the slope is the component of the weight force along the slope. If the slope makes an angle \(\theta=14^{\circ}\) with the horizontal, then the component of the weight force along the slope is \(F = W\sin\theta\).

Step2: Calculate the force

Substitute \(W = 155\) and \(\theta = 14^{\circ}\) into the formula \(F = W\sin\theta\). We know that \(\sin(14^{\circ})\approx0.2419\). Then \(F=155\times\sin(14^{\circ})\).

$$F = 155\times0.2419=37.4945$$

Answer:

\(37.4945\)