A block is moving on a frictionless floor in the positive x-axis direction with an initial velocity of 12 m/s. A constant force of 30 N directed along the negative x-axis acts on the block, and at the end of 8 s the block moves with a velocity of 4 m/s in the negative x-direction. Find the mass of the body.
Question
A block is moving on a frictionless floor in the positive x-axis direction with an initial velocity of 12 m/s. A constant force of 30 N directed along the negative x-axis acts on the block, and at the end of 8 s the block moves with a velocity of 4 m/s in the negative x-direction. Find the mass of the body.
Solution 1
To find the mass of the body, we first need to find the acceleration of the body. We know that acceleration is the change in velocity over time.
The initial velocity of the block is 12 m/s in the positive x-axis direction. After 8 seconds, the block is moving with a velocity of 4 m/s in the negative x-axis direction. So, the change in velocity is -12 m/s - (-4 m/s) = -16 m/s.
The time over which this change occurs is 8 seconds. So, the acceleration of the block is -16 m/s / 8 s = -2 m/s². The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which is what we expect since the force is acting in the negative x-axis direction.
Next, we use Newton's second law, which states that the force acting on an object is equal to the mass of the object times its acceleration. Rearranging this equation to solve for mass gives us mass = force / acceleration.
The force acting on the block is 30 N, and the acceleration we found is -2 m/s². So, the mass of the block is 30 N / -2 m/s² = -15 kg.
The negative sign indicates that the direction of the force is opposite to the direction of the acceleration, which is what we expect since the force is acting in the negative x-axis direction. However, mass is a scalar quantity and cannot be negative. Therefore, the mass of the block is 15 kg.
Solution 2
To find the mass of the body, we first need to find the acceleration of the body. We know that acceleration is the change in velocity over time.
The initial velocity of the block is 12 m/s in the positive x-direction. After 8 seconds, the block is moving with a velocity of 4 m/s in the negative x-direction. So, the change in velocity is -12 m/s - (-4 m/s) = -16 m/s.
The time over which this change occurs is 8 seconds. So, the acceleration of the block is -16 m/s / 8 s = -2 m/s². The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which is what we expect since the force is acting in the negative x-direction.
We know that force is equal to mass times acceleration (F = ma). We can rearrange this equation to solve for mass (m = F/a).
The force acting on the block is 30 N, and the acceleration we found is -2 m/s². So, the mass of the block is 30 N / -2 m/s² = -15 kg.
The negative sign indicates that the direction of the force is opposite to the direction of
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