A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?

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Hi, everyone in this particular practice problem, we are being asked to determine the spring constant. We will have a 3.5 kg block placed on the talked about spring compressing it to 25 centimeters. And the spring is originally at equilibrium which is 33 centimeter long and is placed vertically with one N fixed on the ground. We're being asked to calculate the spring constant and the options given are a 137 Newton per centimeter. B 137 Newton per meter. C 429 Newton per centimeter and D 429 Newton per meter. So we will consider the block to be steady and not moving. Hence, because of this, the net force acting on the block is then going to be zero. So we can apply Newton's second law to this particular problem with the force by the spring acting upwards while the gravitational pull acting downwards. So according to Newton's second law, the sigma or the net force sigma F in the Y direction in this case is going to equals to zero Newton. So the Sigma forces there will be two different forces which is the force by the spring acting upwards and the gravitational force acting downwards. So in this case, Sigma F Y is going to be F spring minus F block equals to zero Newton. So F spring is essentially going to be negative K multiplied by delta Y and F block is then going to be just the gravitational weight of the B block which is M multiplied by G of that will be equals to zero Newton. So rearranging this, we will get negative K delta Y equals to M multiplied by G. And we want to get the K in this case, which is the spring constant and rearranging this, we will get K equals to M multiplied by G divided by negative delta Y just like. So, so M in this case is the mass of the block. G is the gravity shell acceleration and delta Y is the compression in the spring. Uh In this case, delta Y is going to equals to the final uh length which is 25 centimeters minus the original one which is 33 centimeter. So delta Y is then going to equals to negative eight centimeter or essentially delta Y equals to negative 0.8 m just like. So therefore, we can then substitute everything into our K E equation which will then becomes K equals to M multiplied by G M is the 3. kg multiplied by G which is 9.81 m per second squared. All of that is going to then be divided by negative delta Y which is negative of negative 0.8 m just like so and rounding everything up, we will then get K to equals to 429 Newton per meter just like. So, so 429 Newton per meter is then going to be the spring constant in this particular practice problem which will correspond to option D. So option D is going to be the answer to this particular practice problem with a spring constant of 429 Newton per meter. So that will be all for this particular practice problem. If you guys still have any sort of confusion, please make sure to check out our other lesson videos and that will be it for this one. Thank you.

A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?

Verified Solution

Key Concepts

Hooke's Law

Spring Constant (k)

Gravitational Force