Four movers pick up boxes. Each box has a different mass, and each mover applies a different amount of force to lift the box. Which box will have the greatest acceleration?(1 point)
Responses
a 20 kg box lifted with 40 N of force
a 20 kg box lifted with 40 N of force
a 10 kg box lifted with 60 N of force
a 10 kg box lifted with 60 N of force
a 20 kg box lifted with 60 N of force
a 20 kg box lifted with 60 N of force
a 10 kg box lifted with 40 N of force
a 10 kg box lifted with 40 N of force
The box that will have the greatest acceleration is a 10 kg box lifted with 60 N of force.
The box with the greatest acceleration will be determined by the net force applied to the box. The net force is calculated by subtracting the force of gravity from the applied force. The force of gravity on the box can be calculated using the formula: mass * acceleration due to gravity.
Let's calculate the net force for each scenario:
1. For the first scenario, a 20 kg box lifted with 40 N of force:
Net force = 40 N - (20 kg * 9.8 m/s^2) = 40 N - 196 N = -156 N
2. For the second scenario, a 10 kg box lifted with 60 N of force:
Net force = 60 N - (10 kg * 9.8 m/s^2) = 60 N - 98 N = -38 N
3. For the third scenario, a 20 kg box lifted with 60 N of force:
Net force = 60 N - (20 kg * 9.8 m/s^2) = 60 N - 196 N = -136 N
4. For the fourth scenario, a 10 kg box lifted with 40 N of force:
Net force = 40 N - (10 kg * 9.8 m/s^2) = 40 N - 98 N = -58 N
The box with the greatest acceleration will be the one with the greatest net force. Looking at the calculations above, we can see that the third scenario, a 20 kg box lifted with 60 N of force, has the greatest net force (-136 N), and hence, the greatest acceleration.
To determine which box will have the greatest acceleration, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
Let's calculate the acceleration for each box:
Box 1: Mass = 20 kg, Force = 40 N
Acceleration = Force / Mass = 40 N / 20 kg = 2 m/s^2
Box 2: Mass = 10 kg, Force = 60 N
Acceleration = Force / Mass = 60 N / 10 kg = 6 m/s^2
Box 3: Mass = 20 kg, Force = 60 N
Acceleration = Force / Mass = 60 N / 20 kg = 3 m/s^2
Box 4: Mass = 10 kg, Force = 40 N
Acceleration = Force / Mass = 40 N / 10 kg = 4 m/s^2
From the calculations, we can see that Box 2, which has a mass of 10 kg and is lifted with 60 N of force, will have the greatest acceleration of 6 m/s^2.