Mindblown: a blog about philosophy.
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Horizontal Force
You want to slowly push a stiff board across a 20 cm gap between two tabletops that are at the same height. If you apply only a horizontal force, how long must the board be so that it doesn’t tilt down into the gap before reaching the other side? This is a conceptual problem. The board needs…
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Spring Constant
Experiments using “optical tweezers” measure the elasticity of individual DNA molecules. For small enough changes in length, the elasticity has the same form as that of a spring. A DNA molecule is anchored at one end, then a force of 1.5 nN (1.5 x 10-9 N) pulls on the other end, causing the molecule to stretch by 5.0…
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What is the Value of the Spring Constant?
You need to make a spring scale to measure the mass of objects hung from it. You want each 1.5cm length along the scale to correspond to a mass difference of 0.10 kg. What should be the value of the spring constant? Known In a spring scale: F = mg = kx Solve for k: k = mg/x…
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Force to be Motionless in Position
A man is attempting to raise a 7.5 m-long, 35 kg flagpole that has a hinge at the base by pulling on a rope attached to the top of the pole, as shown in the figure below. With what force does the man have to pull on the rope to hold the pole motionless in this position? The…
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Angular Acceleration and Revolutions
The crankshaft in a race car goes from rest to 3500 rpm in 3.5 seconds. What is the crankshaft’s angular acceleration? Known Variables: time: 3.5 seconds angular frequency(ω): 3500 rpm We know that the angular acceleration formula is as follows: α= ω/t First we need to convert ω into proper units which is in radians/second. 3500 rpm…
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What Force Must You Pull
The tune-up specifications of a car call for the spark plugs to be tightened to a torque of 35 Nm. You plan to tighten the plugs by pulling on the end of a 21-cm-long wrench.Because of the cramped space under the hood, you’ll need to pull at an angle of 125° with respect to the wrench shaft. With what force must…
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What is the Torque?
Tom and Jerry both push on the 3.10 m-diameter merry-go-round shown in the figure. If Tom pushes with a force of 39.3 and Jerry pushes with a force of 35.5 , what is the net torque on the merry-go-round? Known variables: diameter: 3.10 m or radius: 1.55 m Force_1= 39.3 N Force_2: 35.5 N Force_1 angle: 60° Force_2 angle: 80° First off, we…
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What is the Magnitude of the Torque?
An athlete at the gym holds a 4.0 kg steel ball in his hand. His arm is 70 cm long and has a mass of 4.0 kg. 1) What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Known Variables: Mass of Arm: 4 kg…
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Distance from the Center of Gravity of a Object
Two thin beams are joined end-to-end as shown in the figure to make a single object. (The object is seen from the side.) The left beam is 11.3 kg and 1.00 m long and the right one is 41.0 kg and 2.00 m long. How far from the left end of the left beam is the center of gravity of the…
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Moment of Inertia
A regulation table tennis ball has a mass of 2.5 g and is 42 mm in diameter. What is its moment of inertia about an axis that passes through its center? Known Variables: m: 2.5 g or .0025 kg d: 42 mm or .042 m r= .042/2 = .021m Moment of Inertia for a hollow sphere I =(2/3) x m x r²…
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