Question

question 3
you have a plank 0.45 m long. you lift up one end.34 m. what angle (in degrees) above the horizontal does your plank make?
add your answer
integer, decimal or e notation allowed

question 4
you are pushing on a 10 kg chair with a force of 52 n, but it does not move? what is the magnitude of the static friction force in newtons?
add your answer
integer, decimal or e notation allowed

Explanation:

Question 3

Step1: Identify the trigonometric relationship

We can consider a right - triangle where the length of the plank is the hypotenuse \(c = 0.45\space m\) and the height it is lifted is the opposite side \(a=0.34\space m\). The sine function is given by \(\sin\theta=\frac{a}{c}\).

Step2: Calculate the sine of the angle

Substitute \(a = 0.34\) and \(c = 0.45\) into the sine formula: \(\sin\theta=\frac{0.34}{0.45}\approx0.7556\).

Step3: Find the angle

To find \(\theta\), we use the inverse sine function \(\theta=\sin^{- 1}(0.7556)\). Using a calculator, \(\theta\approx49.1^{\circ}\).

Step1: Apply Newton's first law

Since the chair is not moving (in equilibrium), the net force in the horizontal direction is zero. Let the applied force be \(F = 52\space N\) and the static friction force be \(f_s\). According to Newton's first law \(F_{net,x}=\sum F_x=0\).

Step2: Relate the applied force and static friction force

\(F - f_s=0\) (because the applied force and static friction force are in opposite directions in the horizontal plane). So, \(f_s=F\).

Answer:

\(49.1\)

Question 4