Sample Problem 1 The coefficient of static friction between a person's shoe and the ground is 0.70. Determine the maximum magnitude of acceleration of the 62 kg person, if he starts running on a horizontal surface from rest. Given: μ = 0.70; m = 62 kg s Required: a Analysis: Draw the FBD of the person (Figure 7). FN Figure 7 Fax In this case, the max force since the norm need to calculate F he mace of Foet=FF Solution: Fs = μg. (0. F = 42 Now calculate the m Fnet ma (62 kg) a FS 425 425 a 6.9 = Statement: The maxi 6.9 m/s². Practice 1. Two people start running from rest. The first person has a mass of 59 kg and is wearing dress shoes with a coefficient of static friction of 0.52. The other person is wearing running shoes with a coefficient of static friction of 0.66. (a) Calculate the maximum possible initial acceleration of the person wearing dress shoes. [ans: 5.1 m/s² [forward]] (h) Explain why we do not really need poreon whon finding the initial

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Sample Problem 1
The coefficient of static friction between a person's shoe
and the ground is 0.70. Determine the maximum magnitude
of acceleration of the 62 kg person, if he starts running on a
horizontal surface from rest.
Given: μ = 0.70; m = 62 kg
Required: a
Analysis: Draw the FBD of the person (Figure 7).
F₁
Figure 7
Fax
In this case, the maximum force of static friction is the net
force since the normal force and gravity cancel. First we
need to calculate F
Fnet = F F = μSFN
Solution: F= μSFN
Fμmg
- (0.70) (62 kg) (9.8 m/s²)
FS 425.3 N (two extra digits carried)
Now calculate the magnitude of the acceleration:
=
Fnet = FS
ma =
425.3N
(62 kg) a = 425.3 N
a = 6.9 m/s²
Statement: The maximum magnitude of the acceleration is
6.9 m/s².
Practice
1. Two people start running from rest. The first person has a mass of 59 kg and is wearing
dress shoes with a coefficient of static friction of 0.52. The other person is wearing
running shoes with a coefficient of static friction of 0.66.
(a) Calculate the maximum possible initial acceleration of the person wearing dress
shoes. [ans: 5.1 m/s²³ [forward]]
(b) Explain why we do not really need the mass of either person when finding the initial
maximum possible acceleration.
(c) Determine the ratio of the two accelerations and compare it to the ratio of the two
coefficients of friction. [ans: 0.79; they are equal
Transcribed Image Text:Sample Problem 1 The coefficient of static friction between a person's shoe and the ground is 0.70. Determine the maximum magnitude of acceleration of the 62 kg person, if he starts running on a horizontal surface from rest. Given: μ = 0.70; m = 62 kg Required: a Analysis: Draw the FBD of the person (Figure 7). F₁ Figure 7 Fax In this case, the maximum force of static friction is the net force since the normal force and gravity cancel. First we need to calculate F Fnet = F F = μSFN Solution: F= μSFN Fμmg - (0.70) (62 kg) (9.8 m/s²) FS 425.3 N (two extra digits carried) Now calculate the magnitude of the acceleration: = Fnet = FS ma = 425.3N (62 kg) a = 425.3 N a = 6.9 m/s² Statement: The maximum magnitude of the acceleration is 6.9 m/s². Practice 1. Two people start running from rest. The first person has a mass of 59 kg and is wearing dress shoes with a coefficient of static friction of 0.52. The other person is wearing running shoes with a coefficient of static friction of 0.66. (a) Calculate the maximum possible initial acceleration of the person wearing dress shoes. [ans: 5.1 m/s²³ [forward]] (b) Explain why we do not really need the mass of either person when finding the initial maximum possible acceleration. (c) Determine the ratio of the two accelerations and compare it to the ratio of the two coefficients of friction. [ans: 0.79; they are equal
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