A man whose mass is 80kg stands on a weighing machine inside a lift. when the lift starts accelerating upwards, the reading of the weighing machine was observed to be 96kg. Determine the upward acceleration of the lift.
Well, it seems like this man has gained a few extra kilograms just from riding the lift! I guess we can call it the "elevator diet." Anyway, let's find the upward acceleration of the lift.
We can use Newton's second law of motion: F = ma, where F is the net force, m is the mass, and a is the acceleration. In this case, the net force is the force exerted by the man on the weighing machine.
Initially, the net force is the man's weight, which is F = mg. So, the weight is F = 80 kg x 9.81 m/s² = 784.8 N.
When the lift starts accelerating upwards, the net force increases to F = (m + Δm) * a, where Δm is the increase in weight and a is the acceleration. In this case, the increase in weight is Δm = 96 kg - 80 kg = 16 kg.
Plugging in the values, we have 784.8 N = (80 kg + 16 kg) * a.
Solving for a, we get a = 784.8 N / 96 kg = 8.175 m/s².
So, the upward acceleration of the lift is approximately 8.175 m/s². I hope this answer uplifts your spirits!
To determine the upward acceleration of the lift, we can use Newton's second law of motion:
Force = Mass x Acceleration
Given:
The man's mass (m) = 80 kg
The reading on the weighing machine (F) = 96 kg
Now, let's calculate the force acting on the man inside the lift:
Force = m x g, where g is the acceleration due to gravity (9.8 m/s^2)
Force = 80 kg x 9.8 m/s^2
Force = 784 N
Since the weighing machine reads the normal force acting on the man, and the normal force is equal to the force exerted by the man on the weighing machine (F), we have:
F = 784 N
Now, let's calculate the net force acting on the man inside the lift:
Net Force = F - Weight, where Weight = m x g
Net Force = F - (m x g)
Net Force = 784 N - (80 kg x 9.8 m/s^2)
Net Force = 784 N - 784 N
Net Force = 0 N
Since the man is not accelerating vertically (net force = 0 N), the upward force exerted by the lift must be equal to the downward force exerted by gravity. Therefore:
Upward Force = Weight
Let's denote the upward acceleration of the lift as a, then:
Upward Force = m x (g + a)
Weight = 80 kg x (9.8 m/s^2 + a)
96 kg = 80 kg x (9.8 m/s^2 + a)
Dividing both sides by 80 kg:
1.2 m/s^2 = 9.8 m/s^2 + a
Subtracting 9.8 m/s^2 from both sides:
1.2 m/s^2 - 9.8 m/s^2 = a
-8.6 m/s^2 = a
Therefore, the upward acceleration of the lift is -8.6 m/s^2.
To determine the upward acceleration of the lift, we can use the concept of apparent weight.
The apparent weight is the force experienced by an object due to the contact with a scale or a weighing machine. In this case, the man's apparent weight is 96 kg.
Apparent weight can be calculated using the equation:
Apparent weight = Actual weight + (Mass × Acceleration)
In this case, the actual weight of the man is 80 kg. So, we can rewrite the equation as:
96 kg = 80 kg + (80 kg × Acceleration)
Subtracting 80 kg from both sides gives us:
16 kg = 80 kg × Acceleration
Simplifying further:
Acceleration = (16 kg) ÷ (80 kg) = 0.2 m/s²
Therefore, the upward acceleration of the lift is 0.2 m/s².