Two crates, of mass 75 kg and 110 kg, are in contact and at rest on a horizontal surface. A 620-N force is exerted on the 75-kg crate. If the coefficient of kinetic friction is 0.15, calculate (a) the acceleration of the system, and (b) the force that each crate exerts on the other.
(c) Repeat with the crates reversed.
a. M = M1+ M2 = 75 + 110 = 185 kg.
M*g = 185 * 9.8 = 1813 N. = Wt. of crates. = Normal force.
0.15*1813 = 272 N. = Force of kinetic friction.
620-272 = M*a.
348 = 185*a,
a =
b. = Mg*sin A = 1813*sin 0 = 0 = Force parallel to the hor. plane. = Force
that each crate exert on the other.
c. Nothing changed.
To calculate the acceleration of the system, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
(a)
1. Determine the net force acting on the system. To find this, subtract the force of friction from the applied force. The force of friction can be calculated using the formula: force of friction = coefficient of kinetic friction * normal force.
- Given: coefficient of kinetic friction = 0.15, normal force = mass * gravitational acceleration.
- Normal force on the 75-kg crate = 75 kg * 9.8 m/s^2 (gravitational acceleration).
- Normal force on the 110-kg crate = 110 kg * 9.8 m/s^2 (gravitational acceleration).
- Force of friction on the 75-kg crate = 0.15 * normal force on the 75-kg crate.
2. Calculate the net force acting on the system by subtracting the force of friction from the applied force.
- Net force = 620 N - force of friction on the 75-kg crate.
3. Use Newton's second law of motion to find the acceleration of the system.
- Net force = (mass of 75-kg crate + mass of 110-kg crate) * acceleration.
- acceleration = net force / (mass of 75-kg crate + mass of 110-kg crate).
(b)
To find the force that each crate exerts on the other, we need to consider the interaction between the two crates. Since they are in contact and not moving vertically, the force exerted by one crate on the other is equal in magnitude and opposite in direction to the force exerted by the other crate.
- Force exerted on the 75-kg crate by the 110-kg crate is equal to the force exerted on the 110-kg crate by the 75-kg crate.
- The total force exerted on each crate can be calculated by multiplying their respective masses by the acceleration of the system.
(c)
To repeat the calculations with the crates reversed, follow the steps above but swap the masses of the crates in the formulas. The force exerted on each crate will also be different since it depends on the respective masses.