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?
a a 10 kg box lifted with 60 N of force
b a 20 kg box lifted with 60 N of force
c a 20 kg box lifted with 40 N of force
d a 10 kg box lifted with 40 N of force
To determine which box will have the greatest acceleration, we can use Newton's second law of motion: force = mass x acceleration.
Let's calculate the acceleration for each box:
a) For a 10 kg box lifted with 60 N of force:
Acceleration = Force / Mass = 60 N / 10 kg = 6 m/s^2
b) For a 20 kg box lifted with 60 N of force:
Acceleration = Force / Mass = 60 N / 20 kg = 3 m/s^2
c) For a 20 kg box lifted with 40 N of force:
Acceleration = Force / Mass = 40 N / 20 kg = 2 m/s^2
d) For a 10 kg box lifted with 40 N of force:
Acceleration = Force / Mass = 40 N / 10 kg = 4 m/s^2
Therefore, the box with the greatest acceleration is the 10 kg box lifted with 60 N of force (option a).
To determine which box will have the greatest acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for calculating acceleration is:
acceleration = net force / mass
Let's calculate the acceleration for each box:
a) acceleration = 60 N / 10 kg = 6 m/s^2
b) acceleration = 60 N / 20 kg = 3 m/s^2
c) acceleration = 40 N / 20 kg = 2 m/s^2
d) acceleration = 40 N / 10 kg = 4 m/s^2
Based on these calculations, the 10 kg box lifted with 60 N of force (option a) will have the greatest acceleration of 6 m/s^2.
To determine which box will have the greatest acceleration, we need to calculate the net force acting on each box. Acceleration is directly proportional to net force, according to Newton's second law of motion.
The net force can be found by subtracting the force due to gravity from the force applied by the mover. The force due to gravity can be calculated by multiplying the mass of the box by the acceleration due to gravity (standard value: 9.8 m/s^2).
Let's calculate the net force for each box:
a) Net force = Force applied - Force due to gravity
= 60 N - (10 kg x 9.8 m/s^2) = 60 N - 98 N = -38 N
b) Net force = Force applied - Force due to gravity
= 60 N - (20 kg x 9.8 m/s^2) = 60 N - 196 N = -136 N
c) Net force = Force applied - Force due to gravity
= 40 N - (20 kg x 9.8 m/s^2) = 40 N - 196 N = -156 N
d) Net force = Force applied - Force due to gravity
= 40 N - (10 kg x 9.8 m/s^2) = 40 N - 98 N = -58 N
Acceleration is calculated by dividing net force by mass (a = F_net/m).
Using the calculated net forces, let's determine the acceleration for each box:
a) Acceleration = Net force / Mass
= -38 N / 10 kg = -3.8 m/s^2
b) Acceleration = Net force / Mass
= -136 N / 20 kg = -6.8 m/s^2
c) Acceleration = Net force / Mass
= -156 N / 20 kg = -7.8 m/s^2
d) Acceleration = Net force / Mass
= -58 N / 10 kg = -5.8 m/s^2
Based on these calculations, the box with the greatest acceleration is box d, a 10 kg box lifted with 40 N of force, which has an acceleration of -5.8 m/s^2. Keep in mind that acceleration is a vector quantity, so the negative sign indicates the direction of the acceleration.