Ask Question
12 May, 19:36

Now let's apply the work-energy theorem to a more complex, multistep problem. In a pile driver, a steel hammerhead with mass 200 kg is lifted 3.00 m above the top of a vertical I-beam that is to be driven into the ground (Figure 1). The hammer is then dropped, driving the I-beam 7.40 cm farther into the ground. The vertical rails that guide the hammerhead exert a constant 60.0 N friction force on it. Use the work-energy theorem to find

(a) the speed of the hammerhead just as it hits the I-beam and

(b) the average force the hammerhead exerts on the I-beam.

+1
Answers (1)
  1. 12 May, 21:56
    0
    a) v = 7.67

    b) n = 81562 N

    Explanation:

    Given:-

    - The mass of hammer-head, m = 200 kg

    - The height at from which hammer head drops, s12 = 3.00 m

    - The amount of distance the I-beam is hammered, s23 = 7.40 cm

    - The resistive force by contact of hammer-head and I-beam, F = 60.0 N

    Find:-

    (a) the speed of the hammerhead just as it hits the I-beam and

    (b) the average force the hammerhead exerts on the I-beam.

    Solution:-

    - We will consider the hammer head as our system and apply the conservation of energy principle because during the journey of hammer-head up till just before it hits the I-beam there are no external forces acting on the system:

    ΔK. E = ΔP. E

    K_2 - K_1 = P_1 - P_2

    Where, K_2: Kinetic energy of hammer head as it hits the I-beam

    K_1: Initial kinetic energy of hammer head ( = 0) ... rest

    P_2: Gravitational potential energy of hammer head as it hits the I-beam. (Datum = 0)

    P_1: Initial gravitational potential energy of hammer head

    - The expression simplifies to:

    K_2 = P_1

    Where, 0.5*m*v2^2 = m*g*s12

    v2 = √ (2*g*s12) = √ (2*9.81*3)

    v2 = 7.67 m/s

    - For the complete journey we see that there are fictitious force due to contact between hammer-head and I-beam the system is no longer conserved. All the kinetic energy is used to drive the I-beam down by distance s23. We will apply work energy principle on the system:

    Wnet = (P_3 - P_1) + W_friction

    Wnet = m*g*s13 + F*s23

    n*s23 = m*g*s13 + F*s23

    Where, n: average force the hammerhead exerts on the I-beam.

    s13 = s12 + s23

    Hence,

    n = m*g * (s12/s23 + 1) + F

    n = 200*9.81 * (3/0.074 + 1) + 60

    n = 81562 N
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Now let's apply the work-energy theorem to a more complex, multistep problem. In a pile driver, a steel hammerhead with mass 200 kg is ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers