What force has to be exerted on a mass 60kg to give it an acceleration of 10$ms^{-2}$ vertically upwards? [g = 10$ms^{-2}$

Analysis

To solve this problem, we need to understand the forces acting on an object being accelerated vertically. When an object is moved upwards, the applied force must not only overcome the weight of the object (gravity) but also provide the additional force required to produce the specified acceleration.

Concept

According to Newton's Second Law of Motion, the net force ($F_{net}$) acting on an object is the product of its mass ($m$) and its acceleration ($a$):

When an object is moving vertically upwards, the net force is the difference between the applied upward force ($F$) and the downward force due to gravity (weight, $W = mg$).

Rearranging to find the applied force ($F$):

Solution

Step 1: Identify the given values

• Mass ($m$) = 60 kg
• Acceleration ($a$) = 10 $ms^{-2}$
• Acceleration due to gravity ($g$) = 10 $ms^{-2}$

Step 2: Apply the formula Substitute the values into the equation $F = m(g + a)$:

• $F = 60 \times (10 + 10)$
• $F = 60 \times 20$
• $F = 1200 \, N$

Conclusion

The force required to lift the 60kg mass with an upward acceleration of 10 $ms^{-2}$ is 1200 N.

Exam Tip: Always remember that when an object accelerates upwards, you add the acceleration to gravity ($g + a$). If the object were accelerating downwards, you would subtract the acceleration from gravity ($g - a$). This simple distinction is a common trap in JAMB Physics questions!