A 60kg body stands on a scale on elevator the elevator starts moving and records 450N find the acceleration of the elevator
force= mg+ma=60(9.8 + a)
450/60 = 9.8+a
a= - (it is going down, or falling) 1.5m/s^2 check that.
To find the acceleration of the elevator, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Here's how you can calculate the acceleration:
Step 1: Determine the weight of the body
The weight of an object can be calculated using the formula:
Weight = mass * gravitational acceleration
Given that the mass of the body is 60 kg, and assuming a gravitational acceleration of 9.8 m/s^2, we can calculate the weight of the body:
Weight = 60 kg * 9.8 m/s^2 = 588 N
Step 2: Determine the net force acting on the body
The net force acting on the body in this case is the difference between the normal force exerted by the scale and the weight of the body.
Net Force = Normal Force - Weight
Given that the scale records a force of 450 N and the weight of the body is 588 N, we can calculate the net force:
Net Force = 450 N - 588 N = -138 N
Note that the negative sign indicates that the net force is directed opposite to the motion of the body (downwards in this case).
Step 3: Calculate the acceleration
Now, we can use Newton's second law to find the acceleration. Rearranging the formula, we get:
Net Force = mass * acceleration
Plugging in the values, we have:
-138 N = 60 kg * acceleration
Solving for acceleration, we get:
acceleration = -138 N / 60 kg = -2.3 m/s^2
Therefore, the acceleration of the elevator is approximately -2.3 m/s^2. The negative sign indicates that the elevator is moving downwards.
To find the acceleration of the elevator, we need to use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
Given:
Mass of body (m) = 60 kg
Force recorded by the scale (F) = 450 N
We can rearrange the formula to solve for acceleration (a):
a = F/m
Substituting the given values:
a = 450 N / 60 kg
Calculating the acceleration:
a = 7.5 m/s^2
Therefore, the acceleration of the elevator is 7.5 m/s^2.