A crane is used to hoist a 500kg crate vertically at a constant velocity of 4 meters per second. Ignore the effects of friction. a) calculate the magnitude of the net force experienced by the crate b) calculate the magnitude of the force applied by the cable on the crate
To calculate the magnitude of the net force experienced by the crate, we need to employ Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this scenario, the crate is moving at a constant velocity. Since acceleration is the rate of change of velocity, and the velocity remains constant, the acceleration is zero.
a) Magnitude of the net force experienced by the crate:
Net Force = Mass * Acceleration
Since the acceleration is zero, the net force is also zero.
Therefore, the magnitude of the net force experienced by the crate is 0 N.
Now, let's move on to calculating the magnitude of the force applied by the cable on the crate.
b) Magnitude of the force applied by the cable on the crate:
Since the velocity is constant, we know that the upward force applied by the cable on the crate must be equal to the downward force due to the crate's weight. This is because the crate is not accelerating, so the net force must be zero.
The weight of an object is given by the equation:
Weight = Mass * Gravitational Acceleration
Here, the mass of the crate is given as 500 kg, and the gravitational acceleration is approximately 9.8 m/s² (assuming we are near the Earth's surface).
Weight = 500 kg * 9.8 m/s²
Weight = 4900 N (Newtons)
Therefore, the magnitude of the force applied by the cable on the crate is 4900 N.