Forces and Motion Worksheets - 15 Worksheets Library - Free Printable
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Step-by-step solution for: Forces and Motion Worksheets - 15 Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Forces and Motion Worksheets - 15 Worksheets Library
Here are the step-by-step solutions for the mechanics problems on the worksheet.
1. Mass of the object
* Formula: Force = Mass × Acceleration ($F = ma$). To find mass, we rearrange it to: Mass = Force / Acceleration.
* Calculation: $500 \text{ N} / 10 \text{ m/s}^2 = 50$.
* Answer: The mass is 50 kg.
2. Time to stop
* Logic: The car is slowing down (decelerating) from 30 m/s at a rate of 5 m/s every second. We need to find how many seconds it takes to get to 0 m/s.
* Calculation: $30 \text{ m/s} / 5 \text{ m/s}^2 = 6$.
* Answer: It takes 6 seconds.
3. Net force on the box
* Logic: "Net force" means the total force after combining pushes and pulls. Gravity pulls the box down with 100 N. You push it sideways with 50 N. Since these forces are in different directions (down vs. sideways), they don't cancel each other out or add up simply. The net force acting *in the direction of the push* is just the push itself.
* Answer: The net force acting on the box (in the direction of motion) is 50 N.
4. Time to reach the ground
* Formula: Distance = $\frac{1}{2} \times \text{gravity} \times \text{time}^2$ ($d = \frac{1}{2}gt^2$).
* Setup: $20 = \frac{1}{2} \times 10 \times t^2$.
* Calculation:
* $20 = 5 \times t^2$
* Divide by 5: $4 = t^2$
* Square root of 4 is 2.
* Answer: It takes 2 seconds.
5. Object's acceleration
* Formula: Acceleration = Force / Mass ($a = F/m$).
* Calculation: $80 \text{ N} / 20 \text{ kg} = 4$.
* Answer: The acceleration is 4 m/s².
6. Ball's acceleration
* Formula: Acceleration = (Final Velocity - Initial Velocity) / Time.
* Calculation: $(15 \text{ m/s} - 5 \text{ m/s}) / 2 \text{ s}$.
* $10 / 2 = 5$.
* Answer: The acceleration is 5 m/s².
7. Final velocity on frictionless surface
* Logic: The problem states the surface is "frictionless." This means there is no friction to slow the object down, and no other force is mentioned pushing it faster. According to Newton's First Law, an object in motion stays in motion at the same speed unless acted upon by a force.
* Answer: The final velocity is 10 m/s.
8. Ice skater's acceleration
* Formula: Acceleration = Force / Mass ($a = F/m$).
* Calculation: $200 \text{ N} / 60 \text{ kg} = 3.333...$
* Answer: The acceleration is approximately 3.33 m/s².
9. Car's deceleration
* Formula: Acceleration = (Final Velocity - Initial Velocity) / Time.
* Calculation: The car stops, so final velocity is 0.
* $(0 - 25) / 10 = -2.5$.
* Deceleration is just the positive value of negative acceleration.
* Answer: The deceleration is 2.5 m/s².
10. Time to reach maximum height
* Logic: At the very top (maximum height), the rocket stops moving upward for a split second before falling back down. So, the final velocity at the top is 0 m/s. Gravity slows it down at roughly 10 m/s².
* Formula: Time = (Final Velocity - Initial Velocity) / Acceleration due to gravity.
* Calculation: $(0 - 100) / -10 = 10$.
* Answer: It takes 10 seconds.
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Final Answer:
1. 50 kg
2. 6 seconds
3. 50 N
4. 2 seconds
5. 4 m/s²
6. 5 m/s²
7. 10 m/s
8. 3.33 m/s²
9. 2.5 m/s²
10. 10 seconds
1. Mass of the object
* Formula: Force = Mass × Acceleration ($F = ma$). To find mass, we rearrange it to: Mass = Force / Acceleration.
* Calculation: $500 \text{ N} / 10 \text{ m/s}^2 = 50$.
* Answer: The mass is 50 kg.
2. Time to stop
* Logic: The car is slowing down (decelerating) from 30 m/s at a rate of 5 m/s every second. We need to find how many seconds it takes to get to 0 m/s.
* Calculation: $30 \text{ m/s} / 5 \text{ m/s}^2 = 6$.
* Answer: It takes 6 seconds.
3. Net force on the box
* Logic: "Net force" means the total force after combining pushes and pulls. Gravity pulls the box down with 100 N. You push it sideways with 50 N. Since these forces are in different directions (down vs. sideways), they don't cancel each other out or add up simply. The net force acting *in the direction of the push* is just the push itself.
* Answer: The net force acting on the box (in the direction of motion) is 50 N.
4. Time to reach the ground
* Formula: Distance = $\frac{1}{2} \times \text{gravity} \times \text{time}^2$ ($d = \frac{1}{2}gt^2$).
* Setup: $20 = \frac{1}{2} \times 10 \times t^2$.
* Calculation:
* $20 = 5 \times t^2$
* Divide by 5: $4 = t^2$
* Square root of 4 is 2.
* Answer: It takes 2 seconds.
5. Object's acceleration
* Formula: Acceleration = Force / Mass ($a = F/m$).
* Calculation: $80 \text{ N} / 20 \text{ kg} = 4$.
* Answer: The acceleration is 4 m/s².
6. Ball's acceleration
* Formula: Acceleration = (Final Velocity - Initial Velocity) / Time.
* Calculation: $(15 \text{ m/s} - 5 \text{ m/s}) / 2 \text{ s}$.
* $10 / 2 = 5$.
* Answer: The acceleration is 5 m/s².
7. Final velocity on frictionless surface
* Logic: The problem states the surface is "frictionless." This means there is no friction to slow the object down, and no other force is mentioned pushing it faster. According to Newton's First Law, an object in motion stays in motion at the same speed unless acted upon by a force.
* Answer: The final velocity is 10 m/s.
8. Ice skater's acceleration
* Formula: Acceleration = Force / Mass ($a = F/m$).
* Calculation: $200 \text{ N} / 60 \text{ kg} = 3.333...$
* Answer: The acceleration is approximately 3.33 m/s².
9. Car's deceleration
* Formula: Acceleration = (Final Velocity - Initial Velocity) / Time.
* Calculation: The car stops, so final velocity is 0.
* $(0 - 25) / 10 = -2.5$.
* Deceleration is just the positive value of negative acceleration.
* Answer: The deceleration is 2.5 m/s².
10. Time to reach maximum height
* Logic: At the very top (maximum height), the rocket stops moving upward for a split second before falling back down. So, the final velocity at the top is 0 m/s. Gravity slows it down at roughly 10 m/s².
* Formula: Time = (Final Velocity - Initial Velocity) / Acceleration due to gravity.
* Calculation: $(0 - 100) / -10 = 10$.
* Answer: It takes 10 seconds.
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Final Answer:
1. 50 kg
2. 6 seconds
3. 50 N
4. 2 seconds
5. 4 m/s²
6. 5 m/s²
7. 10 m/s
8. 3.33 m/s²
9. 2.5 m/s²
10. 10 seconds
Parent Tip: Review the logic above to help your child master the concept of force problems worksheet.
