Two crates, of mass m1 = 60 kg and m2 = 130 kg, are in contact and at rest on a horizontal surface (Fig. 4-54). A 620 N force is exerted on the 60 kg crate. The coefficient of kinetic friction is 0.15
a)Calculate the acceleration of the system.
b) calculate the force that each crate exerts on the other.
c) Repeat with the crates reversed.
I was able to calculate the acceleration
try 0.5mv*2=mgh
This question didn't post properly. I was able to find the acceleration (1.79m/s^2), having difficulties getting the force. what would "h" be in your equation? to me that symbolizes height and there's no height in this problem.
If you have a, then F=ma
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) Calculate the acceleration of the system:
First, we need to find the net force acting on the system. The net force is the difference between the applied force and the force of friction. The force of friction can be determined using the formula: frictional force = coefficient of friction * normal force.
Given:
- Mass of crate 1 (m1) = 60 kg
- Mass of crate 2 (m2) = 130 kg
- Applied force = 620 N
- Coefficient of kinetic friction = 0.15
To calculate the normal force, we need to consider the weight of both crates. The weight is given by the formula: weight = mass * acceleration due to gravity. Assuming the crates are on Earth, acceleration due to gravity is approximately 9.8 m/s^2.
Weight of crate 1 = m1 * 9.8
= 60 kg * 9.8 m/s^2
= 588 N
Weight of crate 2 = m2 * 9.8
= 130 kg * 9.8 m/s^2
= 1274 N
The normal force is the force exerted by the surface to support the weight of the crates. In this case, since the crates are in contact and at rest on a horizontal surface, the normal force acting on the system is equal to the sum of the weights of both crates: normal force = Weight of crate 1 + Weight of crate 2.
Normal force = 588 N + 1274 N
= 1862 N
Now, we can calculate the force of friction:
Force of friction = coefficient of friction * normal force
= 0.15 * 1862 N
= 279.3 N
To determine the net force:
Net force = Applied force - Force of friction
= 620 N - 279.3 N
= 340.7 N
Next, we can calculate the acceleration of the system:
Acceleration = Net force / Total mass of the system
= Net force / (m1 + m2)
= 340.7 N / (60 kg + 130 kg)
= 340.7 N / 190 kg
≈ 1.794 m/s^2
Therefore, the acceleration of the system is approximately 1.794 m/s^2.
Now, we can move on to calculating the force that each crate exerts on the other.
b) Calculate the force that each crate exerts on the other:
To calculate the force between the crates, we can consider the force of friction acting on each crate. Since the crates are in contact, the force of friction acts between them in opposite directions.
For crate 1:
Force of friction on crate 1 = coefficient of friction * normal force on crate 1
= 0.15 * (Weight of crate 1 + Weight of crate 2)
= 0.15 * (588 N + 1274 N)
≈ 282.3 N
For crate 2:
Force of friction on crate 2 = coefficient of friction * normal force on crate 2
= 0.15 * (Weight of crate 1 + Weight of crate 2)
= 0.15 * (588 N + 1274 N)
≈ 282.3 N
Therefore, the force that each crate exerts on the other is approximately 282.3 N.
c) Repeat with the crates reversed:
If we reverse the position of the crates, the masses of the crates and the force applied remain the same. However, the normal force acting on each crate will change.
For crate 1:
Normal force on crate 1 = Weight of crate 1
= 588 N
For crate 2:
Normal force on crate 2 = Weight of crate 2 + Force of crate 1 on crate 2
= 1274 N + 620 N
= 1894 N
Using the same calculations as before, we can find the force of friction and the net force. The resulting acceleration and the forces each crate exerts on the other will be different.
I hope this explanation helps you understand how to calculate the acceleration and forces in this system. Let me know if you have any further questions!