A wooden crate sits on the floor of a flatbed truck that is initially at rest, and the coefficient of static friction between the crate and the floor of the truck is 0.25. The driver of the truck wants to accelerate to a velocity of 20 m/s within 4.0 s. If he does so, will the crate slide off the back of the truck?
To determine whether the crate will slide off the back of the truck, we need to compare the force of static friction between the crate and the truck floor to the maximum force of static friction that can be exerted.
The maximum static friction force can be calculated using the formula: F(static max) = μ(static) * N
Where:
- F(static max) is the maximum static friction force
- μ(static) is the coefficient of static friction
- N is the normal force between the crate and the truck floor
The normal force acting on the crate can be calculated using Newton's Second Law: N = m * g
Where:
- m is the mass of the crate
- g is the acceleration due to gravity (approximated as 9.8 m/s²)
Given:
- Coefficient of static friction (μ(static)) = 0.25
- Velocity (v) = 20 m/s
- Time (t) = 4.0 s
We need to find out whether the crate will slide off the back of the truck, so we need to calculate the maximum static friction force and compare it to the actual force required to accelerate the crate.
1. Calculate the mass of the crate:
Since we don't have the mass of the crate given, we need more information to proceed. Please provide the mass of the crate, and we can continue solving the problem.